Gaussian pseudo-likelihood estimation for stationary processes on a lattice

Abstract

For a wide class of second-order stationary spatial processes on a lattice, the statistical properties of the maximum Gaussian pseudo-likelihood estimators are studied. The estimators are natural as they imitate the theoretical prototypes of spatial best linear prediction. Under certain conditions, their asymptotic normality is established with the elements of the asymptotic variance matrix being simple functions of the variable auto-covariances. A short simulation study and a data example favor the use of the Gaussian pseudo-likelihood when the spatial covariance dependence is to be estimated.